Yamabe-harmonic flow on locally conformally flat manifolds

作     者：Zihao WANG 

作者机构：School of Mathematics and Statistics Wuhan University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报(英文版))

年 卷 期：2024年

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by NNSFC (Grant No. 11971358) 

摘      要：In this paper we introduce a new geometric flow consisting of the Yamabe flow coupled with harmonic heat flow of a function on a closed manifold M, or shortly Yamabe-harmonic flow. It is define by ■ To begin with we establish the short-time extsience via conformal transformation for any smooth initial data. Furthermore we derive interior-in-time derivative estimates for the Riemannian curvature and Lapse function and obtain the global existence of Yamabe-harmonic flow. Moreover, compact gradient Yamabe-harmonic solitons are proved to be manifolds with R=φ=Constant. Eventually we obtain the classification of singularities by blow-up rate of AC curvature, which is analogous to that of Ricciharmonic flow and Ricci-connection flow. The relationship between singularity models and solitons shall appear in forthcoming work.